Anyonic correlation functions in Chern-Simons matter theories

Using a novel relation between the parity-even and -odd parts of a correlator, we show that the threepoint function of conserved or weakly broken currents in three-dimensional conformal field theory (CFT) can be obtained from just the free fermion (FF) or the free boson (FB) theory. In the special case of large N Chern-Simons matter theories, we obtain the correlator in terms of a coupling constant dependent "anyonic phase" factor. This anyonic phase factor was previously obtained in the 2 -> 2 exact S-matrix result and is consistent with strong-weak duality. By varying the coupling constant, the CFT correlator interpolates nicely between the same in the FF and FB theories.